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Re: Re: Suggestion: Visualization of complex functions with Mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg44899] Re: Re: Suggestion: Visualization of complex functions with Mathematica
• From: "Peltio" <peltio at twilight.zone>
• Date: Sun, 7 Dec 2003 06:03:45 -0500 (EST)
• References: <bqkb3v$hkt$1@smc.vnet.net> <200312051031.FAA09156@smc.vnet.net> <bqs93e$i15$1@smc.vnet.net>
• Reply-to: "Peltio" <peltioNOSP at Miname.com.invalid>
• Sender: owner-wri-mathgroup at wolfram.com

"Murray Eisenberg" wrote

>What is the correct URLs for the ones listed below: www.kfunigratz.ac.at
>is not being found.

I apologize.
The correct URL (I checked it out now) is
http://www.kfunigraz.ac.at/imawww/vqm/pages/dlgraph.html

While searching the web for the correct address, I've also found the
following packages that can be used to plot complex functions (I'm sure that
there are many more). Some are new to me, but the original poster might find
them interesting enough to try'em out.
They can be reached by using the author name, the package name in Google
(www.google.com) For example fill in the search field with "ComplexPlot.m"
or "complex mathematica filetype:m".

Complex.m by Goeran Andersson
http://www.funet.fi/pub/sci/math/mathematica/Analysis/Complex.m
    *zListPlot[ zlist, opts] pointplots the complex numbers in zlist.
    *zwPlot[ z, w, {t, tmin, tmax}, opts] plots the complex mapping
     w=f(z), z=z(t).

ComplexPlot.m by Jeff Olson
http://www.ph.utexas.edu/~jdolson/math/ComplexPlot.m
    *ComplexPlot[func, {fx, fy}, {t, tmin, tmax}]
    *ComplexListPlot[{z1, z2, ...}] plots a list of complex numbers.
    *ComplexVectorPlot[func, {xmin, xmax}, {ymin, ymax}]
    *ComplexPartialPlots[func, {xmin, xmax}, {ymin, ymax}]
    *ComplexColorPlot[func, {xmin, xmax}, {ymin, ymax}]
    *ComplexContourPlot[func, {xmin, xmax}, {ymin, ymax}]
    *CartesianMap[f, {x0, x1, (dx)}, {y0, y1, (dy)}] plots the image
     of the cartesian coordinate lines under the function f.
    *PolarMap[f, {r0:0, r1, (dr)}, {phi0, phi1, (dphi)}] plots the
     image of the polar coordinate lines under the function f.

ComplexPlot3D by Kevin McIsaac
   *ComplexPlot3D[fn, {x, x0, x2, (dx)}, {x, x0, x2, (dx)}, (options)]
   Plots in the complex plane. The absolute value is represented
   by the height and the phase is represented by the color

ComplexMap by Roman Maeder
    *CartesianMap[f, {x0, x1, (dx)}, {y0, y1, (dy)}] plots the image
     of the cartesian coordinate lines under the function f.
    *PolarMap[f, {r0:0, r1, (dr)}, {phi0, phi1, (dphi)}] plots the
    image of the polar coordinate lines under the function f.

Transform2DPlot by Xah Lee
http://www.xahlee.org/SpecialPlaneCurves_dir/MmaPackages_dir/Transform2DPlot
_dir/Transform2DPlot.m
    This package exports the function Transform2DPlot and
    Transform2DGraphics that plot the image of the plane under
    arbitrary transformation function f:R^2->R^2 or f:C^1->C^1.
    It can be easily adapted to make it plot conformal maps.
    It is possibile to write a shell that calls the procedures with a
    syntax similar to that of ComplexMap. (years ago I wrote one,
    only a few lines long - no big deal since Xah Lee's procedures do
    it all. If someone is interested, though, and has already
    downloaded the original package by Xah Lee let me know and
    I'll send it to them)

ComplexMapPlot by Theodore W. Gray and Jerry Glynn
    This one is included in their book "Exploring Mathematics with
    Mathematica", Addison-Wesley, 1991. I don't think it is
    available on the web. I had found a reference to it in a gallery
    of complex functions (I saved it in rtf format without the
    pictures!!! How smart : )). But if the original poster has access to
    the book he can find out if what it does suits him.

cheers,
Peltio
Invalid address in reply-to. Crafty demunging required to mail me.

• Follow-Ups:
  • Re: Re: Re: Suggestion: Visualization of complex functions with Mathematica
    • From: Murray Eisenberg <murray@math.umass.edu>

• References:
  • Re: Suggestion: Visualization of complex functions with Mathematica
    • From: "Peltio" <peltio@twilight.zone>